In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. ...

‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.

for some positive constant ε depending only on δ. Sometimes we call f a δ-approximate solution of (1.1) and g ε-close to f . Such an idea of stability was given by Ulam [13] for Cauchy equation f(x+y) = f(x)+f(y) and his problem was solved by Hyers [4]. Later, the Hyers-Ulam stability was studied extensively (see, e.g., [6, 8, 10, 11]). Moreover, such a concept is also generalized in [2, 3, 12]...

in this paper, we use the denition of fuzzy normed spaces givenby bag and samanta and the behaviors of solutions of the additive functionalequation are described. the hyers-ulam stability problem of this equationis discussed and theorems concerning the hyers-ulam-rassias stability of theequation are proved on fuzzy normed linear space.

In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.